We analyze diffusion in dilute binary fluids confined within porous media near the critical point of the solvent species. Both ordered and random confining structures are considered. At the solvent critical point solvent dynamics are quiescent, a consequence of the critical slowing-down phenomenon predicted by theory. Solute diffusion, however, remains finite at these conditions, which we have characterized in terms of a system-invariant quantity we define as Omega. In specific situations Omega can also be related to scaling results in pure, homogeneous fluids, a result we illustrate with simulation data for a lattice-gas system. The implications of these theoretical concepts for both short-time dynamics and the practical situation involving diffusion through porous membranes are discussed and illustrated with computer simulation data. The simulations are carried out using a recently proposed relaxation-dynamics simulation algorithm that appears to be ideally suited for dynamical simulations in near-critical systems. (C) 2003 American Institute of Physics.